@sross90,
I think in this, there are two things you need to consider:
- what's best for you; and
- what's best for your kids
I don't think you need to consider what's best for your wife, as she has already left you (maybe not officially, but effectively). That's not to say you need to be nasty or disrespectful to her...just that she has made her choice, you are no longer a couple, and so you no longer have to do what's best for her as well as you.
What's best for you starts with you accepting your situation:
I think you need to understand just how over it is. A woman does
not date another man in front of you, and she definitely does
not introduce the new man to the kids if there is any chance whatsoever that the two of you will get back together. She's told you it's over...but you still want to be married, you still live in the same house while she dates, and you give her money that she's no doubt using to date other men...
...it;s rather screwed up.
However, you seem terrified of getting a divorce. It doesn't seem like you've resolved the effect your parents divorce had on you (not a criticism - we all have ghosts)...and it doesn't seem like you realise how much it's affecting your judgement regarding divorce, and how you wish to be treated / what you are prepared to put up with.
If it helps, there are plenty of children for whom divorce is not terrible...so long as the adults behave as adults. In divorcing, parents can sometimes teach their children that people change, that you can grow apart despite your best intentions, that you can have respectful fights and eventually realise you just disagree too much...
...but in staying in the same house, are you teaching your children how to be walked over? Are you helping confusd them over how relationships should work (knowing that most children learn most about relationships / conflict management / life / self worth etc from their parents)? Ie. is it truly better for your children to stay in such an environment?
Hope it helps some
Best wishes